Abstract
Based on semi-direct sums of Lie subalgebra B and G, two higher-dimensional 4×4 and 6×6 matrix Lie algebra sμ(4) and sμ(6) are constructed with the help of the known Lie algebra A1. Two hierarchies of integrable coupling nonlinear equations with three potentials are proposed, which are derived from coupled discrete four-by-four and six-by-six matrix spectral problems. Moreover, the corresponding 3-Hamiltonian forms are deduced for each lattice equation in the resulting hierarchy by means of the discrete variational identity and two strong symmetry operators of the resulting hierarchy are given. finally, we prove that the hierarchies of the resulting Hamiltonian equations are all Liouville integrable discrete Hamiltonian systems.
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